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A sharp bound on the L2 norm of the solution of a random elliptic difference equation
sharp bound L2 norm random elliptic difference equation
2015/7/14
We consider a stationary solution of the Poisson equation (λ − Lω)φλ(x; ω) = −∂∗b(x; ω), where λ > 0 and Lω is a random, discrete, elliptic operator given by Lωu(x) := ∂&...
Global Existence of Solutions for the Cauahy Problem of the Kawahara Equation with $L^2$ Initial Data
Kawahara equation Cauchy problem global solution
2007/12/11
In this paper we study solvability of the Cauchy problem of the Kawahara equation $\partial_tu+au\partial_xu+\beta\partial^3_xu+\gamma\partial^5_xu =0$ with $L^2$ initial data. By working on the Bourg...
Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices
Kawahara equation Cauchy problem global solution almost conservation law
2007/12/11
We first prove that the Cauchy problem of the Kawahara equation, $\partial_tu+u\partial_xu+\beta\partial_x^3u+\gamma\partial_x^5u=0,$ is locally solvable if the initial data belong to $H^{r}(\bf{R})...